Theorems · Definition · functional analysis

SchwartzMap.evalCLM

(𝕜 : Type u_2) →
  (E : Type u_5) →
    {F : Type u_6} →
      (G : Type u_7) →
        [inst : NormedAddCommGroup E] →
          [inst_1 : NormedSpace ℝ E] →
            [inst_2 : NormedAddCommGroup F] →
              [inst_3 : NormedSpace ℝ F] →
                [inst_4 : NormedField 𝕜] →
                  [inst_5 : NormedAddCommGroup G] →
                    [inst_6 : NormedSpace ℝ G] →
                      [inst_7 : NormedSpace 𝕜 G] →
                        [inst_8 : SMulCommClass ℝ 𝕜 G] → F → SchwartzMap E (F →L[ℝ] G) →L[𝕜] SchwartzMap E G

The map applying a vector to Hom-valued Schwartz function as a continuous linear map.

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Basic

Cited by

5 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedFieldNormedAddCommGroupNormedSpaceNormedSpaceSMulCommClass